An infinite number of effectively infinite clusters are predicted at the percolation threshold, if "effectively infinite" means that a cluster's mass increases with a positive power of the lattice size L. All these cluster masses increase as LD with the fractal dimension D = d - β/v, while the mass of the rth largest cluster for fixed L decreases as l/rλ, with λ = D/d in d dimensions. These predictions are confirmed by computer simulations for the square lattice, where D = 91/48 and λ = 91/96.
- Infinite clusters
- Size distribution
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics